New Math 2

Last week I took our two dobermans for a walk, it looked like this:

On the surface, it looks like a pretty nice walk in the mountains.  The route is scenic with nice elevation loss and gain and the views are pretty nice.  Adding to the reality of our idyllic little dog walk included details like the fact that we were on an unplowed 4 wheel drive road in January during a snowy stretch with an elevation over 9,000 ft and oh yes, my pack weighed 58#.  Thankfully the wind was only 15-20 mph and gusty.  It's a funny thing to have some body parts sweating while others are cold at the same time.  Aah more practice suffering. 

It's on these little jaunts that I think about lots of things basically to take my mind off the hard work, which brings me back to math.  If you've read the previous blog titled New Math, you'll remember that I developed a revolutionary mathematical concept for mountaineering effort or work.  Now, like all great minds before me, I received feedback on my thesis both positively and negatively.  I would like to take this moment and remind my engineering friends that I basically made this stuff up while in a physically induced hallucinatory haze and wrote it down while drinking wine.

Okay now that the air is clear, let's get back to the math.  There were two comments that I thought were interesting and worthy of further evaluation.  The first was from a friend's father who suggested the PFM formula should account for a person's weight in a more fair manner to somehow normalize the effort.  His argument is that a heavier person will appear to have performed less work carrying the same pack weight as a lighter person. 

Now there are a few ways to look at this argument.  In a pure engineering sense, I agree that a straightforward "work" formula neglecting the person's weight matches textbook theories more closely.  If the heavier person is in worse shape than the lighter person, the effort would be the same or even harder because of the additional body weight.  But someone like Hulk Hogan who weighs over 300# of pure muscle in his prime, carrying the same 50# pack as me at 175# would have a much easier time of it. 

So I think the first thing is to establish a criteria for using the PFM formula which states that for a reasonably athletic and fit person, mountaineering work can be expressed as:

Mountaineering Work = [(Body Wt+Load Wt)/Body Wt] Pounds x Elevation Gained in Feet x  Miles walked or Run = PFM

 Here's an example from a run I did last weekend:

This is the mountain run near our house.  Seems straight forward enough and we've seen it before.  But how about this part:

I did it three times last Saturday, first with Mocha, next with Tessa and the last loop by myself.  Obviously the plan was flawed because I should have saved the ever loving pulling machine Tessa for the last loop.  Stats for this bit of weekend exercise are 7.62 miles, 1,881 ft elevation gain and 1:34 to complete including about 3 minutes for dog swapping.  It was hard!

Mountaineering Work =  14,418 PFM

This was one of my hardest workouts with second highest PFM rating and it only took 94 minutes!

As is my habit, when the going gets tough, my brain does funny things.  During one of the more lucid parts of the run, I was thinking about the other feedback I received from a friend we'll call LW.  Now just for a little background, LW is one of my more physically exuberant friends.  She's the type of person who travels around the country running marathons for fun, trains for and participates in triathlons during all sorts of weather and basically likes to torture herself as much or more than I do. 

LW's comment related to the absence of a time factor in the Mountaineering Work formula.  She said that it's obviously harder to the same task faster than it is slower.  Of course I initially received this comment as an affront since she can run faster, bike faster swim faster and probably do most everything faster than I can.  But after letting it stew for a while and then thinking about it again as I was running mountain loops, I realized what she was really getting at.  It's a level of effort thing not just a speed thing.  I've been passed by people much older than I am while running races and they seem to be hardly working while I'm breathing hard just trying to maintain pace. 

Sorting through the idea while ascending the steep hill during the second loop, I could feel the heartbeat in my neck and realized I was pushing hard and my pulse was pretty high.  Could that be it?  What if there was a factor related to heart rate (level of effort) that was included in the formula?  It would have to account for normal resting heart rate and there would need to be an averaging over the duration of activity.  Without going crazy, my conclusion during the next downhill was to add a factor which is simply:

Average Working Heart Rate / Resting Heart Rate

Based on the original Mountaineering Work formula, you would get the same result if the three loops were done at a casual stroll taking 3 hours or more as you do with the 94 minute run.  Aha, LW was definitely onto something.

So now, let's rework the numbers with the heart rate factors.  My resting heart rate is about 58 and during the run I've estimated from a couple checks that it averaged about 145.  The new factor is then 145/58 = 2.5 and the total mountaineering work for the triple loop run is an impressive 36,045 PFM!

Ha, it's just a number but that makes me feel pretty good.  Training is going well.  Kriss joins me on the weekends and some mornings and I usually have company during weightlifting sessions at Pipestone.  Treadmill time is my own and I try not to stare at the View of the World from the Summit of Mt. Everest photo too hard.  I'll see that view for myself soon enough....

Training Statistics

Miles Climbing and Running - 299
Elevation Gain - 80,129 ft
Push-ups - 5,021
Sit-ups - 6,250
Weightlifting - 24 hours
Mountaineering Work (No HR Factor) - 344,140

Off to Russia!

The highest mountain on the European continent is Mt. Elbrus at 18,510ft.  It's situated in a wild and mountainous region called the Greater Caucasus range which runs from northwest at the Black Sea to southeast at the Caspian Sea and generally forms the border between Russia and Georgia.

For someone who grew up during the cold war, traveling to this part of the world has a special meaning.  My first job out of college was designing nuclear submarines for use against our number one enemy the Soviet Union.  Now I was traveling to a remote part of Russia to climb a famous mountain.  It's strange how things change over time.

The jumping off spots for Elbrus are the small mountain towns of Terskol and Cheget.  Traveling to this region required a stopover in St. Petersburg which is a beautiful city and worthy of bucket list status.  After a couple days experiencing Russian culture, we flew to a small town called Mineralnye Vody and took a van ride for 5 hours past multiple sketchy roadside checkpoints.  Arriving in the mountain region, we came to a lodge in Terskol and were happy to have a home and be on foot for a while.

We spent the next few days taking hikes and exploring the local region.  the scenery was strikingly beautiful and rugged.  One day, we hiked up an old ski area and got a nice view of Mt. Elbrus in the distance with it's distinctive double summit.

After a few days of acclimatization hikes, gear sorting and eating well, it was time for the main event.  There's a small ski area on the flanks of Mt. Elbrus so why not take our backpacks on the lift and get a ride up to 12,000ft?  In some ways it felt a little like cheating but really, where's the challenge in hiking up a trail for a few thousand feet?  Arriving at the top, we had a couple mile trek to a small hut with two bunk rooms and an eating area.  These were high class accommodations although sleeping in the same room with 6 or 7 other people takes patience and ear plugs.

The lower part of the mountain was surprisingly warm during the day and we wore short sleeves during an acclimatization hike up to the Pastukhov Rocks.  Shown below is the well-oiled Colorado team.

The next day was summit day.  Unlike previous big mountain climbs, we didn't stay in multiple camps on Elbrus.  Everything above 13,000ft or so is open country and very exposed.  Summit day is a huge 5,000 foot plus effort from the hut.  Unfortunately our day started with winds in the 40 mph range well before sunrise and continued for the entire day with gusts over 60 mph.  Wind direction was basically in our faces all day and it really took a toll both physically as well as mentally.  Remember previous explanations about practicing suffering?  This is why.

Photos cannot convey the miserable nature of our summit day but maybe the look of the ground blizzard above gives some indication.  We trudged up the broad slope, stopping only briefly a couple of times to take a quick drink, eat a snack and add a layer on the way to the saddle between the two summits.  Lingering any longer and the cold seeps through your layers and into your bones.

At the saddle, we rope up for the exposed ascending traverse.  We're a good 5 or 6 hours into it by now and the notorious wind is unyielding.  Finally after another 90 minutes or so, we reach the summit.  The photos below could be from any miserable snow covered summit well above treeline on any continent in the world, but it was Elbrus and Alan, Debby, Kriss & I had it all to ourselves.

The descent is generally the most dangerous part of any big climb.  Fatigue is setting in and the inspirational pull of the summit is replaced by the realization that you've still got a long way to go before getting back down to camp.  Descending the traverse in high winds with shifting snow under foot and significant steep exposure to our left requires a high intensity focus.  As the anchor at the back of the rope, I'm watching everyone's feet, hyper aware that one misstep could rip our team off the mountain and send us sliding down the steep slope. 

Thankfully we reach the saddle without incident, stow the rope into my pack and continue the slog back to the hut and a hot meal.  This was the biggest summit push so far in our experience and we feel good about our accomplishment.  Without the wind, it would have been tough but enjoyable.  We found out later that wind on Elbrus is one of the biggest factors for teams not reaching the summit.  

Back from the climb, we had the chance to view Mt. Elbrus one last time from across the valley.  What a striking view of a beautiful mountain!

Training Ramps Up!

A big part of success in the mountains starts months before the climb.  While training for any sport takes time, discipline and fortitude, mountaineering seems to require a significant amount of suffering, both during training as well as during the actual climb.  I assume this is true for other sports as well, when the participant is looking to achieve the very best that they can but my experience in over exertion lies in the mountains mostly. 

Many friends have mentioned living vicariously through my mountaineering adventures over the years.  Those climbs included a few stories and photos, including the summit shot of course but no real depth so here's a look at some of my training routines.

St. Mary's Glacier
Local hikes and climbs are fun and we do lots of them for training, exercise and overall enjoyment.  What better way to train for climbing mountains than to climb mountains?  A little while ago, Kriss and I went up for a quick climb of St, Mary's Glacier and beyond depending on how it goes.  It was a particularly energizing day as you can see below

We had some nice new snow and there was about a foot of powder on the trail.  The temperature was a balmy 18 degrees at the car so let's just say it was less than that on the glacier.  Oh and yes there was just a little bit of wind, maybe 20 mph sustained with those gusts that stand you up and halt all forward progress when they slam into your chest.  I think that happens at about 60 mph.  A couple of miles up, we decided that was enough.

What usually happens to me when climbing with a heavy backpack is a general dissension within the ranks of my clothes in the area around the waist.  It all starts off great but then the pants slide down and all the upper layers begin to ride up, under the backpack waist belt.  Eventually a gap develops between the bottom edge of all the upper body layers and the top edge of all the lower body layers.  This particular day was no different but I really didn't notice until we turned around and the first 60 mph gust hit me from behind...    

Mornings at Pipestone
Most mornings I begin the day at Pipestone at about 6:30 with a brisk walk on the treadmill.  It's a simple 45-60 minute workout which starts with putting on my old friend the Denali Pro backpack.  It's got a variety of things in it including two tents, a climbing rope and a few dumbbells.  Total weight right now is about 45#.

I start the treadmill at a 5% grade and within a few minutes it's topped out at 10% with gradual speed increases all the way up to 4mph (15 min pace for you runners).  The result includes heavy breathing, lots of sweating and worked legs.  Exactly what's needed on a regular basis.  Note the photo in front of the treadmill.  It's titled "The World From the Summit of Mt Everest"

James Peak Today
This morning was beautiful so we headed out for a climb of James Peak.

Feeling pretty strong, I threw an extra pair of boots into my training pack along with another water bottle.  Total weight, 58#.  The climb started reasonably enough with the usual steep slope but thankfully a complete lack of wind.  Oh, what a beautiful day this will be I thought.  It's a rare treat to be up high without getting blown around.  Kriss was also feeling good and we had high hopes that the morning clouds would lift.

A few miles into the climb, we noticed the air was starting to feel damp and the clouds were lowering to meet us.  We could still see slivers of mountains in the distance rising above the trees and into the clouds.

Hitting the steep slopes of James Peak, I began to wonder about the judgment displayed earlier within the warm confines of our house.  There, with a warm cup of coffee to drink and walking around in my slippers, it sounded like a great idea to throw a few random things into the top of that cavernous Gregory pack.  Now, at 12,500' and climbing a 45 degree slope, my back and hips are complaining.  But, like a good mountaineer, I realize the value in suffering for practice so onward we went for a few more hundred vertical feet until we hit our turnaround time.

It's just as well that we were done.  We were climbing in the clouds with visibility of about 100 ft and a breeze was starting to develop.

Running loops and thinking about math
Yesterday I decided to take our dogs for a run.  They're both fully grown exuberant Dobermans and the roads around our house are snow packed so the prudent thing was to take each separately for a loop around the mountain.





Tessa is absolutely crazy and pulls like a Clydesdale so most of the first loop was spent in self preservation mode.  Mocha on the other hand is a pretty good boy unless we see cars or other dogs.  Of course we saw two cars and one other dog who happened to be running loose and was interested in our little adventure.  At one point I was dragging my boy up a steep hill to create separation between the two dogs.  More good training I guess!  After that, we had an uneventful couple of miles together and my mind turned back to the New Math post and all of the good feedback I received from my fellow engineering geek friends.  One suggestion had me puzzled and I finally worked out a suitable solution worthy of an equation revision.  Stay tuned for New Math 2.

Training Statistics
Just for fun, I've been keeping a spreadsheet.  I know that's a surprise to most of you who know me but please don't post any comments.  Here are a few totals to ponder:

Miles Climbing and Running - 264
Elevation Gain - 68,516 ft
Push-ups - 4,171
Sit-ups - 4,000
Weightlifting - 16 hours